The HSBC Services Purchasing Managers' Index (PMI), compiled by Markit, nudged up to 47.2 last month from 47.1 in October.
The improvement, coupled with the positive findings of Monday's survey on Indian manufacturing, augurs well for Asia's third-largest economy, which grew at a higher-than-expected 4.8 percent annual rate in the three months through September.
"Service sector activity remains subdued, but would at least appear to be stabilising," said Leif Eskesen, chief economist for India at survey sponsor HSBC.
While the services PMI reading was a little better than the previous month, it has now spent five straight months below the 50 mark that divides contraction from growth, prompting firms to freeze hiring plans.
The employment sub-index fell to 49.9 in November from 50.1.
Although the survey pointed to the softness in demand leveling off, a complete recovery is still some way off.
New business in November fell at a slightly slower pace than in October, but it was the fifth month running that demand has declined.
For inflation, the survey showed a mixed picture, with firms ramping up their prices faster despite some moderation in rising input costs.
Wholesale price inflation rose to an eight-month high in October - making it the fifth straight month above the Reserve Bank of India's perceived comfort level of 5 percent - raising the prospect for fresh rate hikes.
To try and control stubbornly high inflation, the Reserve Bank of India has raised interest rates by half a percentage point since September.